3 papers
math.GM2020
A group theoretic proof of Frobenius' theorem
Liguo He, Congru Xu
Let G be a Frobenius group with the Frobenius kernel N. Applying character theory, G. Frobenius proved that N was a normal subgroup of G in the year 1901. This is a celebrated appl…
math.RA2019
A new proof of an equality associated with submatrices and eigenvector elements
Liguo He, Guirong Song
By using the methods of Cauchy-Binet type formula and adjugate matrix respectively, a wonderful equality relating to the elements of eigenvectors, the eigenvalues and the submatrix…
math.GR2019
Group-theoretic remarks on Goldbach's conjecture
Liguo He, Xianyu Hu
The famous strongly binary Goldbach's conjecture asserts that every even number can always be expressible as the sum of two distinct odd prime numbers. We use a new app…